Using trial and error. There are 2 solutions to it and may be more.
2 4 4 2
1 4 4 2
+ 5 4 4 2
----------
9 3 2 6
4 1 1 4
5 1 1 4
+ 0 1 1 4
----------
9 3 4 2
We have to fill number from 1 to 12 at the intersection point of two or more lines. We have to construct a star using two triangle. The sum of all number lying in straight lines should be same. This can be easilty understood by the fig. and hence solved.
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We have one answer where sum of all the numbers lying in straight lines is 26.
If you have others, do submit them.
